136 Query

course Mth 152

風ÕHö­í‰Â¯éY“—éUÆ{–N Ñassignment #019

019. `query 19

Liberal Arts Mathematics II

03-20-2009

......!!!!!!!!...................................

13:50:55

`questionNumber 190000

query problem 13.6.9 wt vs ht 62,120; 62,140; 63,130; 65,150; 66,142; 67,13068,175; 68,135; 70,149; 72,168. Give the regression equation and the predicted weight when height is 70.

......!!!!!!!!...................................

RESPONSE -->

y' = 3.35x - 78.4

156lb

.................................................

......!!!!!!!!...................................

13:51:04

`questionNumber 190000

** The equation is obtained by substituting the weights for y and the heights for x in the formula for the regression line.

You get

y = 3.35 x - 78.4.

To predict weight when height is 70 you plug x = 70 into the equation:

y = 3.35 * 70 - 78.4.

You get

y = 156,

so the predicted weight for a man 70 in tall is 156 lbs. **

......!!!!!!!!...................................

RESPONSE -->

ok

.................................................

......!!!!!!!!...................................

13:51:42

`questionNumber 190000

**** query problem 13.6.12 reading 83,76, 75, 85, 74, 90, 75, 78, 95, 80; IQ 120, 104, 98, 115, 87, 127, 90, 110, 134, 119

......!!!!!!!!...................................

RESPONSE -->

y = -193x + 15800

.................................................

......!!!!!!!!...................................

13:51:53

`questionNumber 190000

**

n = 10

sum x = 811

sum x ^2 = 66225

sum y = 1104

sum y^2 = 124060

sum xy = 90437

a = [10(90437) - (811)(1104)] / [10(66225) - (811^2)] = 1.993

a = 1.99

b = [1104 - (1.993)(811) / 10 = -51.23

y' = 1.993x - 51.23 is the eqation of the regression line.

**

......!!!!!!!!...................................

RESPONSE -->

ok

.................................................

......!!!!!!!!...................................

13:52:50

`questionNumber 190000

**** query problem 13.6.15 years 0-5, sales 48, 59, 66, 75, 80, 89

What is the coefficient of correlation and how did you obtain it?

......!!!!!!!!...................................

RESPONSE -->

r = .996

Use coefficient equation.

.................................................

......!!!!!!!!...................................

13:52:56

`questionNumber 190000

**STUDENT SOLUTION:

X Y XY X^2 Y^2

0 48 0 0 2304

1 59 59 1 3481

2 66 132 4 4356

3 75 225 9 5626

4 80 320 16 6400

5 90 450 25 8100

Sums=

15 418 1186 55 30266

The coefficient of the correlation: r = .996

I found the sums of the following:

x = 15, y = 418, x*y = 1186, x^2 = 55

n = 6 because there are 6 pairs in the data

I also had to find Ey^2 = 30266

I used the following formula:

r = 6(1186) - 15(418) / sq.root of 6(55) - (15)^2 * sq. root of 6(30266) - (418)^2 =

846 / sq. root of 105 * 6872 = 846 / sq. root of 721560 = 846 / 849.4 = .996 **

......!!!!!!!!...................................

RESPONSE -->

ok

.................................................

......!!!!!!!!...................................

13:56:26

`questionNumber 190000

**** query problem 13.6.24 % in West, 1850-1990, .8% to 21.2%

What population is predicted in the year 2010 based on the regression line?

What is the equation of your regression line and how did you obtain it?

......!!!!!!!!...................................

RESPONSE -->

y = 1.44x - .39

y = 1.44(16) - .39 = 22.65%

Plug into equation.

.................................................

......!!!!!!!!...................................

13:56:33

`questionNumber 190000

** STUDENT SOLUTION:

Calculating sums and regression line:

n = 8

sum x = 56

sum x^2 = 560

sum = 77.7

sum y^2 = 1110.43

sum xy = 786.4

a = 1.44

b = -.39

r = .99

In the year 2010 the x value will be 16.

y' = 1.44(16) - .39 = 22.65.

There is an expected 22.65% increase in population by the year 2010. **

......!!!!!!!!...................................

RESPONSE -->

ok

.................................................

&#Very good responses. Let me know if you have questions. &#